Panel Regression Model

Dan Ovando

October 21, 2015

The Panel Regression Model

Why a Panel Regression?

Advantages of Panel Data

Advantages of Panel Data

Costello et al. 2008

Back to PRM

Why don’t we care about Causation?

Why don’t we care about Causation?

PRM Methods

\[log(\frac{B}{B_{msy}})_{i,y} = \alpha + \beta{X_{i}} + \gamma{Y_{i,y}} + \epsilon_{s} + e_{i,y,s}\]

Summary of the Data

The Data

The Data

The Data

The Models

Model 1
Dependent variable:
LogBvBmsy
YearsBack 0.01***
(0.001)
ScaledCatch 0.29*
(0.16)
ScaledCatch1Back 0.20
(0.17)
ScaledCatch2Back 0.07
(0.17)
ScaledCatch3Back 0.04
(0.16)
ScaledCatch4Back -0.12
(0.13)
MaxCatch 0.0000*
(0.0000)
TimeToMaxCatch 0.02***
(0.001)
InitialScaledCatchSlope -4.05***
(0.41)
MeanScaledCatch 0.63***
(0.16)
CatchToRollingMax 0.91***
(0.10)
MaxLength 0.0005**
(0.0002)
AgeMat 0.03***
(0.005)
VonBertK -0.18*
(0.10)
Temp 0.03***
(0.01)
SpeciesCatNameFlounders, halibuts, soles 0.72***
(0.07)
SpeciesCatNameHerrings, sardines, anchovies 0.61***
(0.06)
SpeciesCatNameMiscellaneous coastal fishes 0.67***
(0.20)
SpeciesCatNameMiscellaneous demersal fishes 1.17***
(0.10)
SpeciesCatNameMiscellaneous pelagic fishes -0.42***
(0.10)
SpeciesCatNameSharks, rays, chimaeras 0.80***
(0.23)
SpeciesCatNameTunas, bonitos, billfishes 0.44***
(0.09)
Constant -2.75***
(0.11)
Observations 3,240
R2 0.48
Adjusted R2 0.47
Residual Std. Error 0.86 (df = 3217)
F Statistic 132.43*** (df = 22; 3217)
Note: p<0.1; p<0.05; p<0.01

The Models

In log space

The Models

Now exponentiated

The Models

Residuals vs. predicted

The Models

Residuals vs. exponentiated predicted values

The Models

Residuals over time

The Models

Retransformation Bias

Retransformation Bias

Retransformation Bias

We have a few problems

Retransformation Bias

Next Steps